cowboy bebop's pretty unique, the three series that I can think of right now that are most related are outlaw star, trigun, and kiddy grade. that said, you really shouldn't miss full metal alchemist. watch the first few episodes. that kind of series doesn't come along often.

Texhnolyze (Yoshitoshi ABe, designed SE Lain as well)
Lupin III - Castle of Cagliostro (ritchan's DVD9 rip, naturally)
Touch (yes, Touch. I love Touch. Highly recommended over anything else here except:)
Maison Ikkoku (like crack, except that it makes you laugh and slam your fist on the table. Also the shortest Takahashi TV series, so you don't have to clear up too much HDD space just around 20GBs)
Ghost in the Shell (movie), GITS:SAC, GITS:SAC 2nd GiG (if you don't get GITS:SAC or 2nd GiG, try the Laughing Man and Individual Eleven movies, it's ok nobody will blame you for not getting it)
Neon Genesis Evangelion (whole series+movies except games)
ef - a tale of memories/melodies
CLANNAD (funny for the most part, and jerks your tears more often than Kanon did)
Mobile Suit Gundam 00
Mobile Suit Gundam (original Gundam, the one where Amuro was supposed to die halfway but the producers tuned it down for kiddies)
Higurashi no Naku Koro ni, Higurashi no Naku Koro ni Kai (best with the lights turned off)
Deathnote (obviously)
Code Geass (at first I thought it was a DN ripoff, but then I watched it and decided I really don't care. Just lower your expectations for R2)
Sakura Taisen (oldschool, not much depth, but you should watch it for the ending song and general knowledge expansion)
Battle Programmer Shirase (multiplied my interest for rare computers, somehow... must have been the doujin SCSI card)
Suzumiya Haruhi no Yuutsu (to this day, I have an altar of the GAWD Haruhi.... somewhere)
Galaxy Angel (all series except GA Rune, DAMN funny)
Utawarerumono (perhaps, I only played the game, which was good strategy-wise, but I hated some H-scenes)
Fate/Stay Night (the last episode was the worst last episode I've ever watched, but the beginning's great)
Magical Lyrical Nanoha As (well, it's... probably not your cup of tea, but it works, yeah? and it's required for the attachment)
Then finish Ever17: the out of infinity. If you feel like it, go on with Never7, Remember11, and 12Riven. You need Chinese or Japanese to go with the latter three, although there is an English translation project for Remember11.
Then you are ready for the following attachment. EDIT: Come to think of it, wow, that's a lot of anime I've watched there. And it's not even the full list.

_________________
Originally Posted by Tommie
Please delete your post. It is an insult to all the hard work society has put into making you an intelligent being.

Like somebody at AMD said about a decade ago: Benchmarking is like sex. Everybody brags about it, everybody loves doing it and nobody can agree on performance.